My go to romantic DVD is the BBC Colin Firth/Jennifer Ehle version of Pride and Prejudice. I also enjoyed the lastest mini-series version of Emma with Romola Garai and Jonny Lee Miller. And the Richard Armitage/Daniela Denby-Ashe production of North & South (the Elizabeth Gaskell one, not John Jakes though I own both on DVD). And the Emma Thompson/Hugh Grant/Kate Winslet/Alan Rickman version of Sense & Sensibility.

My favorite romantic comedy is Year of the Comet with Tim Daly & Penelope Ann Miller. It has such gorgeous scenery and was filmed in London, Scotland, and France. I don't think it's available on DVD here in the US though.

I also love the romance between Liam Neeson and Debra Winger in Leap of Faith, but not sure that qualifies as the movie is more about Steve Martin's character.

Ridicule me if you will, but I stand by my love of the Sabrina remake with Julia Ormand and Harrison Ford. But recent movies? Nah. The most recent movie I loved was Paul and, while there's a romance in it, in no way is it a romantic movie._________________Angsty romance with scattered humor.
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I will definitely second the recommendations of "Pride and Prejudice" and "North And South" if you are looking for longer more involved romantic mini series. Both are excellent.

If you are looking for something modern and incredibly sweet and old fashioned I would recommend "Return To Me" with David Duchovny and Minnie Driver. It is a throwback to the days of true "romance" movies. I loved how the main characters are not extremely glamorous magazine executives but nice every day people. He owns/runs a construction company and she is a waitress in her grandfather's restaurant (and aspiring artist). Bonnie Hunt wrote it and has a supporting role. I find it really charming and different from all the "friends with benefits" movies out now.

Im Juli (In July)--A German road movie in the spirit of the very first romcom, It Happened One Night. It's funny, sweet, and Moritz Bleibtreu (famous from Lola rennt--Run Lola Run) is fantastic.

My Sassy Girl--A quixotic Korean movie that's crazy weird and hilarious in some spots but heartbreakingly sweet and tender. NB: some versions are in the original Korean, some are dubbed in Chinese; one of these versions has way better subtitles than the other but I can't remember which!

The Fifteen Streets--A British tv movie based on the novel of the same name by Catherine Cookson. Though still not as good as the book, it's one of my favorite movie versions of her novels.

The Sissi Trilogy--German movies from the 50s telling the story of Kaiserin Elisabeth of Austria. They're pure fairy tale from a historical standpoint, but they're beautifully made and Romy Schneider is magical. These movies are seared into the German cinematic conscious the way Gone with the Wind is in the US.

If we're going to suggest vintage movies, I would like to suggest Die Zürcher Verlobung a.k.a. The Affairs of Julie, a German film from 1957, which is one of my favourite romantic movies of all time. This is one of the very few romances where the heroine does not end up with the tall, dark and handsome guy and you don't want her to, either. There's also a trip across Germany and Switzerland in wintertime, a fake engagement to a non-existing fiance and a lot of poking fun at the conventions of romantic comedy in general and German cinema of the 1950s in particular. The literal translation of the German title "The Zurich Engagement" is actually much better than the English title.

Another German film romance from the same period (it even stars the same actress) that I love a lot is Das Wirtshaus im Spessart a.k.a. The Spessart Inn. It's a historical romance of the best sort featuring a dashing highwayman, a beautiful and resourceful comtessa, a shady tavern in the middle of the woods and plenty of crossdressing (heroine dresses as a boy, hero of the secondary romance dresses as a woman). It's actually a musical, but the songs are really good and used to frame/narrate the story via a wandering ballad singer.